Problem

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Tags: geometry, circumcircle, geometry unsolved



Let H be orthocenter and O circumcenter of an acuted angled triangle ABC. D and E are feets of perpendiculars from A and B on BC and AC respectively. Let OD and OE intersect BE and AD in K and L, respectively. Let X be intersection of circumcircles of HKD and HLE different than H, and M is midpoint of AB. Prove that K,L,M are collinear iff X is circumcenter of EOD.